Built-in Mathematica Symbol

AiryBi

AiryBi[z]
gives the Airy function

.

Evaluate numerically:

Evaluate for complex arguments:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

AiryBi threads element-wise over lists and matrices:

Simple exact values are generated automatically:

Find series expansions at infinity:

AiryBi can be applied to power series:

Expansion at infinity for an arbitrary symbolic direction

:

Solve the Schrödinger equation in a linear potential (e.g. uniform electric field):

Check the Sommerfeld radiation condition for a combination of Airy functions:

There is only an outgoing plane wave:

Plot the imaginary part in the complex plane:

Use FullSimplify to simplify Airy functions, here in the Wronskian of the Airy equation:

Compare with the output of Wronskian:

FunctionExpand tries to simplify the argument of AiryBi:

Generate Airy functions from differential equations:

Find a numerical root:

Compare with the built-in function AiryBiZero:

Integrals:

Integral transforms:

Machine-precision input is insufficient to get a correct answer:

Use arbitrary-precision evaluation instead:

A larger setting for $MaxExtraPrecision can be needed:

Machine-number inputs can give high-precision results:

Simplifications sometimes hold only in parts of the complex plane:

Parentheses are required for correct parsing in the traditional form: